The ratio in which the line joining the points $(2, 4, 5)$ and $(3, 5, -4)$ is divided by the $yz$-plane is

$A(3, 2, -1), B(4, 1, 0), C(2, 1, 4)$ are the vertices of a triangle $ABC$. If the bisector of $\angle BAC$ intersects the side $BC$ at $D(p, q, r)$, then $\sqrt{2p + q + r} =$

Let $A(4,3,5), B(1,-2,1), C(3,2,1)$ be the vertices of a triangle $ABC$. If the internal bisector of $\angle BAC$ meets the side $BC$ at $D$, then $CD=$

The coordinates of the point which divides the line segment joining the points $(2, -1, 3)$ and $(4, 3, 1)$ in the ratio $3 : 4$ internally are given by:

Using the section formula,show that the points $A(2, -3, 4)$,$B(-1, 2, 1)$,and $C(0, \frac{1}{3}, 2)$ are collinear.

$A$ point $R$ with $x$-coordinate $4$ lies on the line segment joining the points $P(2, -3, 4)$ and $Q(8, 0, 10)$. Find the coordinates of the point $R$.